The research objective of this paper is to address the critical issue of the reduced survival probability of ballistic missiles due to their limited maneuverability during the penetration interception process. The penetration capability, as the core performance indicator of ballistic missiles, directly affects their battlefield effectiveness. However, existing studies either simplify the non-linear strong coupling characteristics by using linear models, or fail to fully consider the impact of maneuver constraints on the game strategy, resulting in a significant gap between theoretical achievements and actual combat requirements. Especially in complex confrontation scenarios involving multiple interceptor missiles jointly defending, traditional methods are difficult to achieve effective penetration while maintaining stability. Therefore, it is urgently necessary to develop a theoretical framework that integrates non-linear dynamic characteristics, maneuver constraints, and game confrontation, to provide a solution that is both theoretically rigorous and applicable in engineering for the optimization of the penetration trajectory of ballistic missiles in real battlefield environments. This is of great military significance for enhancing strategic deterrence capabilities and breaking through modern air defense systems.

An affine nonlinear differential game model was established, and considering the limited maneuverability, a performance index function containing an integral form of the control energy term was designed. Based on differential game theory, the saddle point control strategy of the game was derived. An evaluation network was designed based on the adaptive dynamic programming algorithm to approximately approximate and solve the differential game strategy. The adaptive update law of the evaluation neural network weights was given, and its stability was derived and proved.

To begin with, to simplify the difficulty of solving, an affine nonlinear differential game system was established, and the action-evaluation neural network result was abandoned. Instead, a single evaluation neural network result was designed to approximate the differential game strategy online. Next, to take into account the limited maneuverability during the process of strategy solving, a performance index function with integral constraints on the control energy term was designed. There exists an explicit expression of the limited maneuverability in the given differential game strategy. Finally, an adaptive update law for the evaluation neural network weights was designed, and the stability of the system was strictly proved theoretically. The simulation results demonstrate the effectiveness of the adaptive dynamic programming solution method for the differential game problem considering limited maneuverability in the "one red and two blue" scenario.

This paper focuses on the numerical solution of differential game problems under limited maneuverability. It designs a performance index function and a differential game model considering limited maneuverability, develops a game strategy under limited maneuverability, and introduces an adaptive dynamic programming algorithm to solve this problem online to obtain the numerical strategy of the differential game. The generated game strategy takes into account the problem of limited maneuverability and effectively achieves the mission of evading and striking ground high-value targets for ballistic missiles.